Problems from competitions for 6-graders

1. The figure shown consists of 8 congruent squares. The perimeter of the figure is 36 units. What is the area of the figure?

2. The cafeteria sells each apple at one price and each banana at another price. For 1 apple and 3 bananas Jose pays $2.05. For 4 apples and 2 bananas April pays $2.70. Maria buys 2 apples and 2 bananas. How much does she have to pay?

3. There are 8-legged spiders and 6-legged flies in a room. The total number of insects is 80. The total number of insect legs is 604. How many more spiders than flies are in the room?

4. A tractor has 14 gallon gasoline tank. The tractor starts with a full tank of gasoline. It runs out of gasoline when it is done plowing 3/5 of a field. How much gallons of gasoline does the tractor need to plow the whole field?

5. If the length of a rectangle is reduced by 50% and the width of the rectangle is increased by 50%, how does the area of the rectangle change?

6. An animal walks 30 feet in 5 seconds. What is the speed of this animal in miles per hour?